We all believe in something and science itself is premised on a whole set of beliefs. Above all, science is founded on the belief that things are comprehensible and that by the ingenuity of our minds and the probing of ever more subtle instruments we will ultimately come to know It All. But is the All inherently knowable? I believe, though I cannot prove it, that there will always be things we do not know—large things, small things, interesting things and important things.

If theoretical physics is any guide we might suppose that science is a march towards a finite goal. For the past few decades theoretical physicists have been searching for a so-called "Theory of Everything," what Nobel laureate Stephen Weinberg has also called a "Final Theory." This "ultimate" set of equations that would tie together all the fundamental forces which physicists recognize today—the four essential powers of gravity, electromagnetism, and the nuclear forces inside the cores of atoms. But such theory—if we are lucky enough to extract it from the current mass of competing contenders—would not tell us anything about how proteins form or how DNA came into being. Less still would it illuminate the machinations of a living cell, or the workings of the human mind. Frankly, a "theory of everything" would not even help us to understand how snowflakes form.

In an age when we have discovered the origin of the universe and observed the warping of space and time it is shocking to hear that scientists do not understand something as "paltry" as the formation of ice crystals. But that is indeed the case.

Kenneth Libbrecht, chairman of the Cal tech physics department is a world expert on ice crystal formation, a hobby project he took on more than twenty years ago precisely because as he puts it "there are six billion people on this planet, and I thought that at least one of us should understand how snow crystals form." After two decades of meticulous experimentation inside specially constructed pressurized chambers Libbrecht believes he has made some headway in understanding how ice crystallizes at the edge of the quasi-liquid layer which surrounds all ice structures. He calls his theory "structure dependent attachment kinetics," but he is quick to point out that this is far from the ultimate answer. The transition from water to ice is a mysteriously complex process that has engaged minds as brilliant as Johannes Kepler and Michael Faraday. Libbrecht hopes he can add the small next step in our knowledge of this wondrous substance that is so central to life itself.

Studying ice crystals is Libbrecht's hobby—in his "day job" he is one of the hundreds of physicists who are working on the LIGO detector which is designed to detect gravitational waves that are believed to emanate from black holes and other massive cosmological entities. Gravity waves have been predicted by the general theory of relativity, and hence physicists believe they must exist. Here the matter of belief has literally bought into being a an extremely expensive machine. Any successful theory of everything will have to account for gravity, the most mysterious of all the forces and the one physicists least understand. Like the other three forces, physicists believe gravity must ultimately manifest itself in both wave and particle forms. LIGO is designed to detect such waves, if indeed they do exist.

Some years ago the science writer John Horgan wrote a marvelously provocative book in which he suggested that science was coming to an end, all the major theoretical edifices now supposedly being in place. Horgan was right in one sense, for high-energy physics may be on the verge of achieving its final unification. But in so many other areas, science is just beginning. Only now are we acquiring the scientific tools and techniques to begin to investigate how our atmosphere works, how ecological systems function, how genes create proteins, how cells evolve, and how brains work. The very success of "fundamental science" has opened doors undreamed of by earlier generations and in many ways it seems there is more than ever that we do not know. At a time when journals tout theories about how to create entire universes it is easy to imagine that science has grasped the whole of reality. In truth our ignorance is vast—and personally I believe it will always be so.

Rather than pretend we will soon know it all, I suggest we might adopt instead the attitude of the great fifteenth century champion of science, Cardinal Nicholas of Cusa. Cusa titled his major work On Learned Ignorance. A complex and poetic fusion of mathematics, scientific speculation and Catholic theology, Cusa puts forward in this book the view that we can never —even in principle—know everything. Only God can do that. We mortals, confined within the world itself can never see it whole, from the outside as it were. But while we cannot know it All, Cusa insists we can know a great deal and that science and mathematics will take our knowledge forward. Our ignorance then can be ever more learned. Not omniscience then, but an ever more subtle and insightful unknowing is the goal that Cusa advocated. In the humble snowflakes Ken Libbrecht studies we have the perfect metaphor for such a view—though they melt on your tongue, each tiny crystal of ice encapsulates a universe whose basic rules we have barely begun to unravel.